Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1960) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.87996\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.87996 | −1.08540 | −0.542698 | − | 0.839928i | \(-0.682597\pi\) | ||||
−0.542698 | + | 0.839928i | \(0.682597\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.534253 | 0.178084 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.29417 | −0.993231 | −0.496615 | − | 0.867971i | \(-0.665424\pi\) | ||||
−0.496615 | + | 0.867971i | \(0.665424\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.19292 | 1.16291 | 0.581453 | − | 0.813580i | \(-0.302484\pi\) | ||||
0.581453 | + | 0.813580i | \(0.302484\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.43737 | −0.348614 | −0.174307 | − | 0.984691i | \(-0.555768\pi\) | ||||
−0.174307 | + | 0.984691i | \(0.555768\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.24445 | −0.285497 | −0.142748 | − | 0.989759i | \(-0.545594\pi\) | ||||
−0.142748 | + | 0.989759i | \(0.545594\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.272828 | 0.0568887 | 0.0284443 | − | 0.999595i | \(-0.490945\pi\) | ||||
0.0284443 | + | 0.999595i | \(0.490945\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.63551 | 0.892104 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.36268 | −0.438739 | −0.219369 | − | 0.975642i | \(-0.570400\pi\) | ||||
−0.219369 | + | 0.975642i | \(0.570400\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.72717 | 0.669420 | 0.334710 | − | 0.942321i | \(-0.391362\pi\) | ||||
0.334710 | + | 0.942321i | \(0.391362\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.19292 | 1.07805 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.169761 | −0.0279085 | −0.0139543 | − | 0.999903i | \(-0.504442\pi\) | ||||
−0.0139543 | + | 0.999903i | \(0.504442\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.88252 | −1.26221 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.6630 | −1.82146 | −0.910730 | − | 0.413001i | \(-0.864480\pi\) | ||||
−0.910730 | + | 0.413001i | \(0.864480\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1458 | 1.54721 | 0.773607 | − | 0.633666i | \(-0.218451\pi\) | ||||
0.773607 | + | 0.633666i | \(0.218451\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.12441 | 0.455743 | 0.227871 | − | 0.973691i | \(-0.426823\pi\) | ||||
0.227871 | + | 0.973691i | \(0.426823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.70220 | 0.378384 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.24701 | −1.27018 | −0.635088 | − | 0.772440i | \(-0.719036\pi\) | ||||
−0.635088 | + | 0.772440i | \(0.719036\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.33952 | 0.309877 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.07107 | −1.18095 | −0.590476 | − | 0.807055i | \(-0.701060\pi\) | ||||
−0.590476 | + | 0.807055i | \(0.701060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.27102 | −0.930958 | −0.465479 | − | 0.885059i | \(-0.654118\pi\) | ||||
−0.465479 | + | 0.885059i | \(0.654118\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.1439 | 1.60579 | 0.802894 | − | 0.596121i | \(-0.203292\pi\) | ||||
0.802894 | + | 0.596121i | \(0.203292\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.512907 | −0.0617467 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.87474 | 0.815882 | 0.407941 | − | 0.913008i | \(-0.366247\pi\) | ||||
0.407941 | + | 0.913008i | \(0.366247\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.2496 | −1.78483 | −0.892414 | − | 0.451218i | \(-0.850990\pi\) | ||||
−0.892414 | + | 0.451218i | \(0.850990\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.9510 | 1.68212 | 0.841061 | − | 0.540940i | \(-0.181931\pi\) | ||||
0.841061 | + | 0.540940i | \(0.181931\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.3173 | −1.14637 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.167199 | 0.0183524 | 0.00917622 | − | 0.999958i | \(-0.497079\pi\) | ||||
0.00917622 | + | 0.999958i | \(0.497079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.44175 | 0.476205 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.09869 | −0.328461 | −0.164230 | − | 0.986422i | \(-0.552514\pi\) | ||||
−0.164230 | + | 0.986422i | \(0.552514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.00694 | −0.726585 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.60894 | 0.671037 | 0.335518 | − | 0.942034i | \(-0.391089\pi\) | ||||
0.335518 | + | 0.942034i | \(0.391089\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.75992 | −0.176879 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.8372 | −1.87437 | −0.937185 | − | 0.348834i | \(-0.886578\pi\) | ||||
−0.937185 | + | 0.348834i | \(0.886578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.46756 | −0.144603 | −0.0723014 | − | 0.997383i | \(-0.523034\pi\) | ||||
−0.0723014 | + | 0.997383i | \(0.523034\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5625 | −1.31114 | −0.655570 | − | 0.755135i | \(-0.727572\pi\) | ||||
−0.655570 | + | 0.755135i | \(0.727572\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.8140 | 1.41893 | 0.709463 | − | 0.704743i | \(-0.248938\pi\) | ||||
0.709463 | + | 0.704743i | \(0.248938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.319144 | 0.0302918 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.1903 | 1.24084 | 0.620418 | − | 0.784271i | \(-0.286963\pi\) | ||||
0.620418 | + | 0.784271i | \(0.286963\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.24008 | 0.207095 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.148415 | −0.0134923 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21.9261 | 1.97701 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.86118 | −0.608831 | −0.304416 | − | 0.952539i | \(-0.598461\pi\) | ||||
−0.304416 | + | 0.952539i | \(0.598461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −19.0736 | −1.67934 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.345708 | 0.0302047 | 0.0151023 | − | 0.999886i | \(-0.495193\pi\) | ||||
0.0151023 | + | 0.999886i | \(0.495193\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.3137 | −0.966595 | −0.483298 | − | 0.875456i | \(-0.660561\pi\) | ||||
−0.483298 | + | 0.875456i | \(0.660561\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.68885 | −0.228066 | −0.114033 | − | 0.993477i | \(-0.536377\pi\) | ||||
−0.114033 | + | 0.993477i | \(0.536377\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.87377 | −0.494661 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.8122 | −1.15503 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.1340 | 1.07598 | 0.537990 | − | 0.842951i | \(-0.319184\pi\) | ||||
0.537990 | + | 0.842951i | \(0.319184\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.01140 | 0.245065 | 0.122532 | − | 0.992465i | \(-0.460898\pi\) | ||||
0.122532 | + | 0.992465i | \(0.460898\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.767920 | −0.0620826 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.4631 | 1.55332 | 0.776662 | − | 0.629918i | \(-0.216911\pi\) | ||||
0.776662 | + | 0.629918i | \(0.216911\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.3840 | 1.37864 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.4922 | −1.05679 | −0.528396 | − | 0.848998i | \(-0.677206\pi\) | ||||
−0.528396 | + | 0.848998i | \(0.677206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.3011 | 0.951889 | 0.475944 | − | 0.879475i | \(-0.342106\pi\) | ||||
0.475944 | + | 0.879475i | \(0.342106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.58057 | 0.352351 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.664852 | −0.0508425 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.48975 | 0.189292 | 0.0946461 | − | 0.995511i | \(-0.469828\pi\) | ||||
0.0946461 | + | 0.995511i | \(0.469828\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.0533 | 1.28180 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.1340 | 1.13117 | 0.565584 | − | 0.824690i | \(-0.308651\pi\) | ||||
0.565584 | + | 0.824690i | \(0.308651\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0637 | −0.822357 | −0.411179 | − | 0.911555i | \(-0.634883\pi\) | ||||
−0.411179 | + | 0.911555i | \(0.634883\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.6692 | 1.01046 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.73495 | 0.346254 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.4517 | −1.62455 | −0.812274 | − | 0.583277i | \(-0.801770\pi\) | ||||
−0.812274 | + | 0.583277i | \(0.801770\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.11482 | −0.224210 | −0.112105 | − | 0.993696i | \(-0.535759\pi\) | ||||
−0.112105 | + | 0.993696i | \(0.535759\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.38765 | −0.0988659 | −0.0494330 | − | 0.998777i | \(-0.515741\pi\) | ||||
−0.0494330 | + | 0.998777i | \(0.515741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.413463 | 0.0293096 | 0.0146548 | − | 0.999893i | \(-0.495335\pi\) | ||||
0.0146548 | + | 0.999893i | \(0.495335\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.7101 | −1.74292 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.145759 | 0.0101310 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.09944 | 0.283564 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.6203 | 1.69493 | 0.847464 | − | 0.530853i | \(-0.178128\pi\) | ||||
0.847464 | + | 0.530853i | \(0.178128\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.9242 | −0.885555 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 28.6686 | 1.93724 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.02678 | −0.405405 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.9065 | −1.19911 | −0.599555 | − | 0.800334i | \(-0.704656\pi\) | ||||
−0.599555 | + | 0.800334i | \(0.704656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.5486 | −0.832878 | −0.416439 | − | 0.909164i | \(-0.636722\pi\) | ||||
−0.416439 | + | 0.909164i | \(0.636722\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8354 | 1.04643 | 0.523215 | − | 0.852201i | \(-0.324732\pi\) | ||||
0.523215 | + | 0.852201i | \(0.324732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.3792 | 1.53162 | 0.765811 | − | 0.643065i | \(-0.222338\pi\) | ||||
0.765811 | + | 0.643065i | \(0.222338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28.1073 | −1.82577 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.9135 | 1.35278 | 0.676390 | − | 0.736544i | \(-0.263544\pi\) | ||||
0.676390 | + | 0.736544i | \(0.263544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.35746 | 0.216273 | 0.108137 | − | 0.994136i | \(-0.465512\pi\) | ||||
0.108137 | + | 0.994136i | \(0.465512\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.48966 | 0.352162 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.21789 | −0.332006 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.314327 | −0.0199197 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.5717 | −1.04600 | −0.522999 | − | 0.852333i | \(-0.675187\pi\) | ||||
−0.522999 | + | 0.852333i | \(0.675187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.898744 | −0.0565036 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.1414 | 0.819737 | 0.409869 | − | 0.912145i | \(-0.365575\pi\) | ||||
0.409869 | + | 0.912145i | \(0.365575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.26227 | −0.0781324 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.75480 | 0.231531 | 0.115765 | − | 0.993277i | \(-0.463068\pi\) | ||||
0.115765 | + | 0.993277i | \(0.463068\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.82542 | 0.356510 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.4952 | −1.00573 | −0.502866 | − | 0.864365i | \(-0.667721\pi\) | ||||
−0.502866 | + | 0.864365i | \(0.667721\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.5420 | 1.36933 | 0.684665 | − | 0.728857i | \(-0.259948\pi\) | ||||
0.684665 | + | 0.728857i | \(0.259948\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.9982 | 0.901154 | 0.450577 | − | 0.892738i | \(-0.351218\pi\) | ||||
0.450577 | + | 0.892738i | \(0.351218\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.99125 | 0.119213 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.0283 | −1.67203 | −0.836014 | − | 0.548709i | \(-0.815120\pi\) | ||||
−0.836014 | + | 0.548709i | \(0.815120\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.1715 | −1.55573 | −0.777866 | − | 0.628430i | \(-0.783698\pi\) | ||||
−0.777866 | + | 0.628430i | \(0.783698\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9340 | −0.878468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.4246 | −0.728340 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.6061 | 0.911716 | 0.455858 | − | 0.890052i | \(-0.349332\pi\) | ||||
0.455858 | + | 0.890052i | \(0.349332\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.2702 | −0.886065 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.14395 | 0.0661562 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 35.4132 | 2.03443 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.3055 | 1.21597 | 0.607984 | − | 0.793949i | \(-0.291978\pi\) | ||||
0.607984 | + | 0.793949i | \(0.291978\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.75895 | 0.156951 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.8799 | 0.843760 | 0.421880 | − | 0.906652i | \(-0.361370\pi\) | ||||
0.421880 | + | 0.906652i | \(0.361370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.16273 | 0.122245 | 0.0611224 | − | 0.998130i | \(-0.480532\pi\) | ||||
0.0611224 | + | 0.998130i | \(0.480532\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.4595 | 1.20528 | 0.602642 | − | 0.798012i | \(-0.294115\pi\) | ||||
0.602642 | + | 0.798012i | \(0.294115\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.78308 | 0.435769 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.4970 | 1.42311 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.78874 | 0.0995282 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.8498 | −1.54010 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.6692 | −0.641399 | −0.320699 | − | 0.947181i | \(-0.603918\pi\) | ||||
−0.320699 | + | 0.947181i | \(0.603918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0906953 | −0.00497007 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1403 | −0.933693 | −0.466846 | − | 0.884338i | \(-0.654610\pi\) | ||||
−0.466846 | + | 0.884338i | \(0.654610\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.7972 | −1.34680 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.2780 | −0.664888 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.20070 | −0.279188 | −0.139594 | − | 0.990209i | \(-0.544580\pi\) | ||||
−0.139594 | + | 0.990209i | \(0.544580\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.8645 | 1.81272 | 0.906362 | − | 0.422501i | \(-0.138848\pi\) | ||||
0.906362 | + | 0.422501i | \(0.138848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.4363 | 1.03743 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.2451 | −1.23721 | −0.618606 | − | 0.785701i | \(-0.712302\pi\) | ||||
−0.618606 | + | 0.785701i | \(0.712302\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.2843 | −1.07056 | −0.535281 | − | 0.844674i | \(-0.679794\pi\) | ||||
−0.535281 | + | 0.844674i | \(0.679794\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4513 | −0.918491 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.279014 | 0.0146445 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.2738 | −0.692887 | −0.346443 | − | 0.938071i | \(-0.612611\pi\) | ||||
−0.346443 | + | 0.938071i | \(0.612611\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.23101 | −0.324373 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.7083 | 1.84891 | 0.924453 | − | 0.381297i | \(-0.124522\pi\) | ||||
0.924453 | + | 0.381297i | \(0.124522\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.90652 | −0.510212 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6878 | −0.651728 | −0.325864 | − | 0.945417i | \(-0.605655\pi\) | ||||
−0.325864 | + | 0.945417i | \(0.605655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.8987 | 0.660823 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.5707 | 1.86867 | 0.934337 | − | 0.356391i | \(-0.115993\pi\) | ||||
0.934337 | + | 0.356391i | \(0.115993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.42040 | 0.275534 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.1085 | 1.52656 | 0.763282 | − | 0.646066i | \(-0.223587\pi\) | ||||
0.763282 | + | 0.646066i | \(0.223587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.392156 | −0.0198322 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.649918 | −0.0327840 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.46756 | −0.374786 | −0.187393 | − | 0.982285i | \(-0.560004\pi\) | ||||
−0.187393 | + | 0.982285i | \(0.560004\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.7331 | −0.585925 | −0.292963 | − | 0.956124i | \(-0.594641\pi\) | ||||
−0.292963 | + | 0.956124i | \(0.594641\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.6277 | 0.778473 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.559222 | 0.0277196 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.8601 | −0.833679 | −0.416840 | − | 0.908980i | \(-0.636862\pi\) | ||||
−0.416840 | + | 0.908980i | \(0.636862\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.2693 | 1.04914 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.05494 | 0.247541 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.3884 | 0.507507 | 0.253753 | − | 0.967269i | \(-0.418335\pi\) | ||||
0.253753 | + | 0.967269i | \(0.418335\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7758 | 0.671393 | 0.335696 | − | 0.941970i | \(-0.391028\pi\) | ||||
0.335696 | + | 0.941970i | \(0.391028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.66923 | 0.0811606 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.9664 | 1.25367 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.4568 | 1.46705 | 0.733527 | − | 0.679661i | \(-0.237873\pi\) | ||||
0.733527 | + | 0.679661i | \(0.237873\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.9182 | 1.24555 | 0.622774 | − | 0.782402i | \(-0.286006\pi\) | ||||
0.622774 | + | 0.782402i | \(0.286006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.339522 | −0.0162415 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.9414 | 1.28584 | 0.642922 | − | 0.765931i | \(-0.277722\pi\) | ||||
0.642922 | + | 0.765931i | \(0.277722\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3858 | 0.778515 | 0.389257 | − | 0.921129i | \(-0.372732\pi\) | ||||
0.389257 | + | 0.921129i | \(0.372732\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.6914 | −1.16786 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.2152 | 0.670858 | 0.335429 | − | 0.942065i | \(-0.391119\pi\) | ||||
0.335429 | + | 0.942065i | \(0.391119\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.4201 | 1.80913 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.66132 | −0.265992 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5093 | 0.678716 | 0.339358 | − | 0.940657i | \(-0.389790\pi\) | ||||
0.339358 | + | 0.940657i | \(0.389790\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.66295 | −0.311000 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.8933 | 0.833374 | 0.416687 | − | 0.909050i | \(-0.363191\pi\) | ||||
0.416687 | + | 0.909050i | \(0.363191\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.2657 | −0.709457 | −0.354729 | − | 0.934969i | \(-0.615427\pi\) | ||||
−0.354729 | + | 0.934969i | \(0.615427\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.5492 | 1.08973 | 0.544863 | − | 0.838525i | \(-0.316582\pi\) | ||||
0.544863 | + | 0.838525i | \(0.316582\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −36.5898 | −1.68597 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −33.4219 | −1.53674 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.94024 | −0.226198 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.65867 | −0.212860 | −0.106430 | − | 0.994320i | \(-0.533942\pi\) | ||||
−0.106430 | + | 0.994320i | \(0.533942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.711794 | −0.0324550 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.5210 | −0.522068 | −0.261034 | − | 0.965330i | \(-0.584063\pi\) | ||||
−0.261034 | + | 0.965330i | \(0.584063\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.3648 | 1.14704 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.2771 | −0.644317 | −0.322158 | − | 0.946686i | \(-0.604408\pi\) | ||||
−0.322158 | + | 0.946686i | \(0.604408\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.39605 | 0.152950 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.9790 | 1.65541 | 0.827703 | − | 0.561167i | \(-0.189647\pi\) | ||||
0.827703 | + | 0.561167i | \(0.189647\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.1256 | −1.03318 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.08985 | −0.360709 | −0.180354 | − | 0.983602i | \(-0.557724\pi\) | ||||
−0.180354 | + | 0.983602i | \(0.557724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.61129 | −0.382441 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.0806 | 1.24465 | 0.622325 | − | 0.782759i | \(-0.286188\pi\) | ||||
0.622325 | + | 0.782759i | \(0.286188\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.76867 | −0.254693 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2924 | −0.452658 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.68063 | −0.205457 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5810 | 0.551182 | 0.275591 | − | 0.961275i | \(-0.411126\pi\) | ||||
0.275591 | + | 0.961275i | \(0.411126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.48453 | −0.0649140 | −0.0324570 | − | 0.999473i | \(-0.510333\pi\) | ||||
−0.0324570 | + | 0.999473i | \(0.510333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.35733 | −0.233369 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9256 | −0.996764 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.84624 | −0.210309 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −48.9022 | −2.11819 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.4513 | −1.22777 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.9135 | 0.813153 | 0.406577 | − | 0.913617i | \(-0.366722\pi\) | ||||
0.406577 | + | 0.913617i | \(0.366722\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.7993 | 0.892583 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.4403 | 0.745693 | 0.372846 | − | 0.927893i | \(-0.378382\pi\) | ||||
0.372846 | + | 0.927893i | \(0.378382\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.88456 | −0.165789 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.94024 | 0.125259 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.2106 | −0.813981 | −0.406990 | − | 0.913432i | \(-0.633422\pi\) | ||||
−0.406990 | + | 0.913432i | \(0.633422\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.5403 | 1.79926 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.90152 | −0.375823 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.7952 | 1.42430 | 0.712150 | − | 0.702028i | \(-0.247722\pi\) | ||||
0.712150 | + | 0.702028i | \(0.247722\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.63635 | 0.194366 | 0.0971830 | − | 0.995267i | \(-0.469017\pi\) | ||||
0.0971830 | + | 0.995267i | \(0.469017\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.8681 | 1.83582 | 0.917912 | − | 0.396785i | \(-0.129874\pi\) | ||||
0.917912 | + | 0.396785i | \(0.129874\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 42.2083 | 1.76328 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.27755 | 0.386230 | 0.193115 | − | 0.981176i | \(-0.438141\pi\) | ||||
0.193115 | + | 0.981176i | \(0.438141\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.85574 | 0.243356 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.4613 | 1.26158 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.9971 | 1.19684 | 0.598420 | − | 0.801183i | \(-0.295796\pi\) | ||||
0.598420 | + | 0.801183i | \(0.295796\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.63829 | −0.191117 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.60873 | 0.107309 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.5228 | −1.04809 | −0.524047 | − | 0.851689i | \(-0.675578\pi\) | ||||
−0.524047 | + | 0.851689i | \(0.675578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.777294 | −0.0318125 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.0364 | 1.26811 | 0.634057 | − | 0.773287i | \(-0.281389\pi\) | ||||
0.634057 | + | 0.773287i | \(0.281389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.56479 | −0.145411 | −0.0727054 | − | 0.997353i | \(-0.523163\pi\) | ||||
−0.0727054 | + | 0.997353i | \(0.523163\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.02219 | 0.285966 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.72620 | −0.273008 | −0.136504 | − | 0.990640i | \(-0.543587\pi\) | ||||
−0.136504 | + | 0.990640i | \(0.543587\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.1004 | 0.529986 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.7422 | 0.797381 | 0.398691 | − | 0.917085i | \(-0.369465\pi\) | ||||
0.398691 | + | 0.917085i | \(0.369465\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.3958 | 0.660069 | 0.330035 | − | 0.943969i | \(-0.392940\pi\) | ||||
0.330035 | + | 0.943969i | \(0.392940\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.5510 | −1.42892 | −0.714458 | − | 0.699678i | \(-0.753327\pi\) | ||||
−0.714458 | + | 0.699678i | \(0.753327\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.26470 | 0.0507506 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.70679 | −0.307780 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.244010 | 0.00972930 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.58569 | −0.381600 | −0.190800 | − | 0.981629i | \(-0.561108\pi\) | ||||
−0.190800 | + | 0.981629i | \(0.561108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −46.2851 | −1.83967 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.67285 | 0.145296 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.5145 | 0.770778 | 0.385389 | − | 0.922754i | \(-0.374067\pi\) | ||||
0.385389 | + | 0.922754i | \(0.374067\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.9895 | −0.748872 | −0.374436 | − | 0.927253i | \(-0.622164\pi\) | ||||
−0.374436 | + | 0.927253i | \(0.622164\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.2570 | 1.62198 | 0.810989 | − | 0.585061i | \(-0.198930\pi\) | ||||
0.810989 | + | 0.585061i | \(0.198930\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.8817 | 1.17296 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.7495 | 0.772857 | 0.386429 | − | 0.922319i | \(-0.373709\pi\) | ||||
0.386429 | + | 0.922319i | \(0.373709\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.14713 | −0.317850 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.1830 | 0.396672 | 0.198336 | − | 0.980134i | \(-0.436446\pi\) | ||||
0.198336 | + | 0.980134i | \(0.436446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.79086 | 0.108552 | 0.0542759 | − | 0.998526i | \(-0.482715\pi\) | ||||
0.0542759 | + | 0.998526i | \(0.482715\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.3301 | 0.440025 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.644606 | −0.0249593 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 33.6636 | 1.30151 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.9520 | 0.924657 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.2879 | −0.704947 | −0.352473 | − | 0.935822i | \(-0.614659\pi\) | ||||
−0.352473 | + | 0.935822i | \(0.614659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.0523 | 0.924404 | 0.462202 | − | 0.886775i | \(-0.347059\pi\) | ||||
0.462202 | + | 0.886775i | \(0.347059\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.5908 | 0.904002 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.2200 | 1.46245 | 0.731224 | − | 0.682137i | \(-0.238949\pi\) | ||||
0.731224 | + | 0.682137i | \(0.238949\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.7699 | −1.13579 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.7720 | −1.47709 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.4623 | −1.00667 | −0.503337 | − | 0.864090i | \(-0.667895\pi\) | ||||
−0.503337 | + | 0.864090i | \(0.667895\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.7641 | 0.634986 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −43.9520 | −1.66242 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.5136 | −1.30356 | −0.651780 | − | 0.758408i | \(-0.725977\pi\) | ||||
−0.651780 | + | 0.758408i | \(0.725977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.211260 | 0.00796780 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.40900 | 0.240695 | 0.120347 | − | 0.992732i | \(-0.461599\pi\) | ||||
0.120347 | + | 0.992732i | \(0.461599\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.98763 | 0.299559 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.01688 | 0.0380824 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.3165 | −1.46830 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.6070 | −1.43980 | −0.719900 | − | 0.694078i | \(-0.755812\pi\) | ||||
−0.719900 | + | 0.694078i | \(0.755812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.31190 | −0.234742 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.5280 | −0.835516 | −0.417758 | − | 0.908558i | \(-0.637184\pi\) | ||||
−0.417758 | + | 0.908558i | \(0.637184\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.6317 | 0.764136 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.5832 | −0.539380 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.50150 | −0.277074 | −0.138537 | − | 0.990357i | \(-0.544240\pi\) | ||||
−0.138537 | + | 0.990357i | \(0.544240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43.2985 | −1.59492 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.0864 | 1.29067 | 0.645336 | − | 0.763899i | \(-0.276717\pi\) | ||||
0.645336 | + | 0.763899i | \(0.276717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.80943 | 0.360358 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.42902 | 0.0891122 | 0.0445561 | − | 0.999007i | \(-0.485813\pi\) | ||||
0.0445561 | + | 0.999007i | \(0.485813\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0893263 | 0.00326828 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.9598 | 0.764833 | 0.382417 | − | 0.923990i | \(-0.375092\pi\) | ||||
0.382417 | + | 0.923990i | \(0.375092\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.1542 | 1.13532 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.9748 | 1.30753 | 0.653763 | − | 0.756699i | \(-0.273189\pi\) | ||||
0.653763 | + | 0.756699i | \(0.273189\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.68960 | 0.0613288 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.45752 | 0.0890852 | 0.0445426 | − | 0.999007i | \(-0.485817\pi\) | ||||
0.0445426 | + | 0.999007i | \(0.485817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −38.0343 | −1.37334 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.6994 | −0.782501 | −0.391250 | − | 0.920284i | \(-0.627957\pi\) | ||||
−0.391250 | + | 0.920284i | \(0.627957\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.7053 | −0.889739 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.6980 | 0.564618 | 0.282309 | − | 0.959324i | \(-0.408900\pi\) | ||||
0.282309 | + | 0.959324i | \(0.408900\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.5141 | 0.520022 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.6466 | −0.810359 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.9522 | −0.391400 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.5074 | −0.873594 | −0.436797 | − | 0.899560i | \(-0.643887\pi\) | ||||
−0.436797 | + | 0.899560i | \(0.643887\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.05887 | −0.251302 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.4868 | −1.08262 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.73557 | 0.203164 | 0.101582 | − | 0.994827i | \(-0.467610\pi\) | ||||
0.101582 | + | 0.994827i | \(0.467610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.49094 | −0.158878 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.65549 | −0.0584937 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.2348 | 1.77275 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.0104 | 1.09162 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.48431 | 0.122502 | 0.0612510 | − | 0.998122i | \(-0.480491\pi\) | ||||
0.0612510 | + | 0.998122i | \(0.480491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.9953 | −0.912819 | −0.456409 | − | 0.889770i | \(-0.650865\pi\) | ||||
−0.456409 | + | 0.889770i | \(0.650865\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −42.3781 | −1.48627 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.6259 | −0.441725 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.4988 | −1.76242 | −0.881210 | − | 0.472725i | \(-0.843271\pi\) | ||||
−0.881210 | + | 0.472725i | \(0.843271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.8699 | 1.56407 | 0.782034 | − | 0.623236i | \(-0.214182\pi\) | ||||
0.782034 | + | 0.623236i | \(0.214182\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.7323 | 0.547066 | 0.273533 | − | 0.961863i | \(-0.411808\pi\) | ||||
0.273533 | + | 0.961863i | \(0.411808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.7726 | 1.79814 | 0.899068 | − | 0.437808i | \(-0.144245\pi\) | ||||
0.899068 | + | 0.437808i | \(0.144245\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.1960 | −0.978109 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.2773 | 0.597192 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.86118 | 0.0987788 | 0.0493894 | − | 0.998780i | \(-0.484272\pi\) | ||||
0.0493894 | + | 0.998780i | \(0.484272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4177 | −0.807508 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 52.6921 | 1.81481 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 49.2014 | 1.68859 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0463156 | −0.00158768 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.8645 | 1.57037 | 0.785185 | − | 0.619261i | \(-0.212568\pi\) | ||||
0.785185 | + | 0.619261i | \(0.212568\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.1501 | −0.790793 | −0.395397 | − | 0.918510i | \(-0.629393\pi\) | ||||
−0.395397 | + | 0.918510i | \(0.629393\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.46384 | 0.288783 | 0.144391 | − | 0.989521i | \(-0.453878\pi\) | ||||
0.144391 | + | 0.989521i | \(0.453878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.0923 | 1.19456 | 0.597278 | − | 0.802034i | \(-0.296249\pi\) | ||||
0.597278 | + | 0.802034i | \(0.296249\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.0753 | 0.953486 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.2513 | −1.67074 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.1115 | 1.86738 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.53085 | 0.119501 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.3372 | −0.652971 | −0.326486 | − | 0.945202i | \(-0.605864\pi\) | ||||
−0.326486 | + | 0.945202i | \(0.605864\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.3388 | −0.989573 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.0573 | 1.11373 | 0.556865 | − | 0.830603i | \(-0.312004\pi\) | ||||
0.556865 | + | 0.830603i | \(0.312004\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.6238 | 0.963267 | 0.481634 | − | 0.876373i | \(-0.340044\pi\) | ||||
0.481634 | + | 0.876373i | \(0.340044\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.1289 | 0.642285 | 0.321142 | − | 0.947031i | \(-0.395933\pi\) | ||||
0.321142 | + | 0.947031i | \(0.395933\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.9871 | 1.13861 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.88818 | −0.130113 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.15058 | −0.0718057 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.80611 | −0.293700 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.2914 | 0.442801 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.9781 | 1.69270 | 0.846350 | − | 0.532627i | \(-0.178795\pi\) | ||||
0.846350 | + | 0.532627i | \(0.178795\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0638 | −0.333796 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.52585 | −0.183080 | −0.0915399 | − | 0.995801i | \(-0.529179\pi\) | ||||
−0.0915399 | + | 0.995801i | \(0.529179\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.550782 | −0.0182282 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.6326 | −1.34035 | −0.670173 | − | 0.742205i | \(-0.733780\pi\) | ||||
−0.670173 | + | 0.742205i | \(0.733780\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −40.0535 | −1.31981 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.8252 | 0.948794 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.784047 | −0.0257515 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.5879 | 0.511423 | 0.255711 | − | 0.966753i | \(-0.417690\pi\) | ||||
0.255711 | + | 0.966753i | \(0.417690\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.9736 | −0.915814 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.4794 | −0.669034 | −0.334517 | − | 0.942390i | \(-0.608573\pi\) | ||||
−0.334517 | + | 0.942390i | \(0.608573\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.06585 | −0.132684 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.7872 | −0.547248 | −0.273624 | − | 0.961837i | \(-0.588222\pi\) | ||||
−0.273624 | + | 0.961837i | \(0.588222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.18201 | −0.103620 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.43928 | 0.111761 | 0.0558807 | − | 0.998437i | \(-0.482203\pi\) | ||||
0.0558807 | + | 0.998437i | \(0.482203\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −63.9402 | −2.07559 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.3430 | −1.30821 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.8610 | 0.999686 | 0.499843 | − | 0.866116i | \(-0.333391\pi\) | ||||
0.499843 | + | 0.866116i | \(0.333391\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.6319 | −0.472982 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.1082 | −0.551877 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.24582 | −0.233493 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.3195 | 1.10364 | 0.551820 | − | 0.833964i | \(-0.313934\pi\) | ||||
0.551820 | + | 0.833964i | \(0.313934\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.36276 | −0.108027 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.6203 | −1.01475 | −0.507373 | − | 0.861727i | \(-0.669383\pi\) | ||||
−0.507373 | + | 0.861727i | \(0.669383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.9454 | 0.606116 | 0.303058 | − | 0.952972i | \(-0.401992\pi\) | ||||
0.303058 | + | 0.952972i | \(0.401992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.2076 | 0.326237 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.91443 | 0.252688 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.2187 | 0.485402 | 0.242701 | − | 0.970101i | \(-0.421967\pi\) | ||||
0.242701 | + | 0.970101i | \(0.421967\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.76805 | 0.0880189 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3069 | 0.994496 | 0.497248 | − | 0.867608i | \(-0.334344\pi\) | ||||
0.497248 | + | 0.867608i | \(0.334344\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.9377 | 0.696172 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.1054 | 1.27015 | 0.635076 | − | 0.772450i | \(-0.280969\pi\) | ||||
0.635076 | + | 0.772450i | \(0.280969\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.786929 | −0.0248973 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9800.2.a.cs.1.1 | 4 | ||
5.4 | even | 2 | 1960.2.a.x.1.4 | ✓ | 4 | ||
7.6 | odd | 2 | 9800.2.a.cl.1.4 | 4 | |||
20.19 | odd | 2 | 3920.2.a.ce.1.1 | 4 | |||
35.4 | even | 6 | 1960.2.q.y.961.1 | 8 | |||
35.9 | even | 6 | 1960.2.q.y.361.1 | 8 | |||
35.19 | odd | 6 | 1960.2.q.x.361.4 | 8 | |||
35.24 | odd | 6 | 1960.2.q.x.961.4 | 8 | |||
35.34 | odd | 2 | 1960.2.a.y.1.1 | yes | 4 | ||
140.139 | even | 2 | 3920.2.a.cd.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.x.1.4 | ✓ | 4 | 5.4 | even | 2 | ||
1960.2.a.y.1.1 | yes | 4 | 35.34 | odd | 2 | ||
1960.2.q.x.361.4 | 8 | 35.19 | odd | 6 | |||
1960.2.q.x.961.4 | 8 | 35.24 | odd | 6 | |||
1960.2.q.y.361.1 | 8 | 35.9 | even | 6 | |||
1960.2.q.y.961.1 | 8 | 35.4 | even | 6 | |||
3920.2.a.cd.1.4 | 4 | 140.139 | even | 2 | |||
3920.2.a.ce.1.1 | 4 | 20.19 | odd | 2 | |||
9800.2.a.cl.1.4 | 4 | 7.6 | odd | 2 | |||
9800.2.a.cs.1.1 | 4 | 1.1 | even | 1 | trivial |